American Institute of Mathematical Sciences

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May  2007, 7(3): 573-580. doi: 10.3934/dcdsb.2007.7.573

On shock waves in solids

James K. Knowles 1,

1. 

Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, United States

Received  August 2006 Revised  January 2007 Published  February 2007

This paper describes some recent theoretical results pertaining to the experimentally-observed relation between the speed of a shock wave in a solid and the particle velocity immediately behind the shock. The new feature in the present analysis is the assumption that compressive strains are limited by a materially-determined critical value, and that the internal energy density characterizing the material is unbounded as this critical strain is approached. It is shown that, with this assumption in force, the theoretical relation between shock speed and particle velocity is consistent with many experimental observations in the sense that it is asymptotically linear for strong shocks of the kind often arising in the laboratory.
Keywords: impact experiments, Shock waves, thermoelastic materials..
Mathematics Subject Classification: Primary: 74J40; Secondary: 74A1.
Citation: James K. Knowles. On shock waves in solids. Discrete & Continuous Dynamical Systems - B, 2007, 7 (3) : 573-580. doi: 10.3934/dcdsb.2007.7.573
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